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The Moore Method in the U.K.: IBL at Birmingham Chris Good, Chris - - PowerPoint PPT Presentation

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The Moore Method in the U.K.: IBL at Birmingham Chris Good, Chris Sangwin, Matthew Badger School of Mathematics University of Birmingham June 2011 Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the

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SLIDE 1

The Moore Method in the U.K.: IBL at Birmingham

Chris Good, Chris Sangwin, Matthew Badger

School of Mathematics University of Birmingham

June 2011

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 1 / 25

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SLIDE 2

Acknowledgements

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 2 / 25

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SLIDE 3

U.K. University Entry

Russell Group, top 20 out of 80 universities. Final year at (high) school: 3 ‘A’ Levels Grades: A∗ (from 2010), A, B, C, (D, E) Maths ‘A’ Level: Pre-calculus, calculus, + stats or mechanics or discrete maths Further Maths ‘A’ Level: more calculus, matrices, complex numbers, stats, mechanics, discrete maths U.K. population is roughly 1/5 that of US ≈ 77K take A Level Maths, 44% get an A ≈ 11K take A level F Maths, 57% get an A

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 3 / 25

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SLIDE 4

U.K. University Entry

Russell Group, top 20 out of 80 universities. Final year at (high) school: 3 ‘A’ Levels Grades: A∗ (from 2010), A, B, C, (D, E) Maths ‘A’ Level: Pre-calculus, calculus, + stats or mechanics or discrete maths Further Maths ‘A’ Level: more calculus, matrices, complex numbers, stats, mechanics, discrete maths U.K. population is roughly 1/5 that of US ≈ 77K take A Level Maths, 44% get an A ≈ 11K take A level F Maths, 57% get an A

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 3 / 25

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SLIDE 5

U.K. University Entry

Russell Group, top 20 out of 80 universities. Final year at (high) school: 3 ‘A’ Levels Grades: A∗ (from 2010), A, B, C, (D, E) Maths ‘A’ Level: Pre-calculus, calculus, + stats or mechanics or discrete maths Further Maths ‘A’ Level: more calculus, matrices, complex numbers, stats, mechanics, discrete maths U.K. population is roughly 1/5 that of US ≈ 77K take A Level Maths, 44% get an A ≈ 11K take A level F Maths, 57% get an A

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 3 / 25

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SLIDE 6

U.K. University Entry

Russell Group, top 20 out of 80 universities. Final year at (high) school: 3 ‘A’ Levels Grades: A∗ (from 2010), A, B, C, (D, E) Maths ‘A’ Level: Pre-calculus, calculus, + stats or mechanics or discrete maths Further Maths ‘A’ Level: more calculus, matrices, complex numbers, stats, mechanics, discrete maths U.K. population is roughly 1/5 that of US ≈ 77K take A Level Maths, 44% get an A ≈ 11K take A level F Maths, 57% get an A

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 3 / 25

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SLIDE 7

U.K. University Entry

Russell Group, top 20 out of 80 universities. Final year at (high) school: 3 ‘A’ Levels Grades: A∗ (from 2010), A, B, C, (D, E) Maths ‘A’ Level: Pre-calculus, calculus, + stats or mechanics or discrete maths Further Maths ‘A’ Level: more calculus, matrices, complex numbers, stats, mechanics, discrete maths U.K. population is roughly 1/5 that of US ≈ 77K take A Level Maths, 44% get an A ≈ 11K take A level F Maths, 57% get an A

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 3 / 25

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SLIDE 8

U.K. University Entry

Russell Group, top 20 out of 80 universities. Final year at (high) school: 3 ‘A’ Levels Grades: A∗ (from 2010), A, B, C, (D, E) Maths ‘A’ Level: Pre-calculus, calculus, + stats or mechanics or discrete maths Further Maths ‘A’ Level: more calculus, matrices, complex numbers, stats, mechanics, discrete maths U.K. population is roughly 1/5 that of US ≈ 77K take A Level Maths, 44% get an A ≈ 11K take A level F Maths, 57% get an A

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 3 / 25

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SLIDE 9

University of Birmingham, U.K.

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 4 / 25

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SLIDE 10

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 5 / 25

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SLIDE 11

University applications process

Each applicant applies to up to 5 universities At Birmingham we ask for

◮ AAA with A in Maths, or ◮ AAB with F

. Maths

1300 SAT + AP Calculus AB at 4/5 (subject requirement) + 2 other APs (≈ AAA at A-level). ≈ 1000 applications for ≈ 200 places Students choose degree programme (major) on application Programmes: 180 students on Single Honours Mathematics (3yr and 4yr); Maths Majors (2/3 Maths, 1/3 other); Joints Honours (eg Maths and Computer Science)

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 6 / 25

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SLIDE 12

University applications process

Each applicant applies to up to 5 universities At Birmingham we ask for

◮ AAA with A in Maths, or ◮ AAB with F

. Maths

1300 SAT + AP Calculus AB at 4/5 (subject requirement) + 2 other APs (≈ AAA at A-level). ≈ 1000 applications for ≈ 200 places Students choose degree programme (major) on application Programmes: 180 students on Single Honours Mathematics (3yr and 4yr); Maths Majors (2/3 Maths, 1/3 other); Joints Honours (eg Maths and Computer Science)

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 6 / 25

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SLIDE 13

University applications process

Each applicant applies to up to 5 universities At Birmingham we ask for

◮ AAA with A in Maths, or ◮ AAB with F

. Maths

1300 SAT + AP Calculus AB at 4/5 (subject requirement) + 2 other APs (≈ AAA at A-level). ≈ 1000 applications for ≈ 200 places Students choose degree programme (major) on application Programmes: 180 students on Single Honours Mathematics (3yr and 4yr); Maths Majors (2/3 Maths, 1/3 other); Joints Honours (eg Maths and Computer Science)

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 6 / 25

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SLIDE 14

University applications process

Each applicant applies to up to 5 universities At Birmingham we ask for

◮ AAA with A in Maths, or ◮ AAB with F

. Maths

1300 SAT + AP Calculus AB at 4/5 (subject requirement) + 2 other APs (≈ AAA at A-level). ≈ 1000 applications for ≈ 200 places Students choose degree programme (major) on application Programmes: 180 students on Single Honours Mathematics (3yr and 4yr); Maths Majors (2/3 Maths, 1/3 other); Joints Honours (eg Maths and Computer Science)

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 6 / 25

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SLIDE 15

University applications process

Each applicant applies to up to 5 universities At Birmingham we ask for

◮ AAA with A in Maths, or ◮ AAB with F

. Maths

1300 SAT + AP Calculus AB at 4/5 (subject requirement) + 2 other APs (≈ AAA at A-level). ≈ 1000 applications for ≈ 200 places Students choose degree programme (major) on application Programmes: 180 students on Single Honours Mathematics (3yr and 4yr); Maths Majors (2/3 Maths, 1/3 other); Joints Honours (eg Maths and Computer Science)

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 6 / 25

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SLIDE 16

University applications process

Each applicant applies to up to 5 universities At Birmingham we ask for

◮ AAA with A in Maths, or ◮ AAB with F

. Maths

1300 SAT + AP Calculus AB at 4/5 (subject requirement) + 2 other APs (≈ AAA at A-level). ≈ 1000 applications for ≈ 200 places Students choose degree programme (major) on application Programmes: 180 students on Single Honours Mathematics (3yr and 4yr); Maths Majors (2/3 Maths, 1/3 other); Joints Honours (eg Maths and Computer Science)

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 6 / 25

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SLIDE 17

Programme Structure

120 credits in 10 credit blocks 100 credits passed at 40% to progress to Yr2 Content of year 1

◮ Calculus (up to integration and ODEs) ◮ Linear Algebra ◮ Abstract Algebra (up to the definition of a group) ◮ Sequences and Series ◮ Mechanics ◮ Statistics ◮ Discrete Maths ◮ Numerics ◮ MOMD

1st yr Calculus and Linear Algebra lectures ≈ 250 students Examples classes 15 to 30 students

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 7 / 25

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SLIDE 18

Programme Structure

120 credits in 10 credit blocks 100 credits passed at 40% to progress to Yr2 Content of year 1

◮ Calculus (up to integration and ODEs) ◮ Linear Algebra ◮ Abstract Algebra (up to the definition of a group) ◮ Sequences and Series ◮ Mechanics ◮ Statistics ◮ Discrete Maths ◮ Numerics ◮ MOMD

1st yr Calculus and Linear Algebra lectures ≈ 250 students Examples classes 15 to 30 students

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 7 / 25

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SLIDE 19

Programme Structure

120 credits in 10 credit blocks 100 credits passed at 40% to progress to Yr2 Content of year 1

◮ Calculus (up to integration and ODEs) ◮ Linear Algebra ◮ Abstract Algebra (up to the definition of a group) ◮ Sequences and Series ◮ Mechanics ◮ Statistics ◮ Discrete Maths ◮ Numerics ◮ MOMD

1st yr Calculus and Linear Algebra lectures ≈ 250 students Examples classes 15 to 30 students

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 7 / 25

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SLIDE 20

Programme Structure

120 credits in 10 credit blocks 100 credits passed at 40% to progress to Yr2 Content of year 1

◮ Calculus (up to integration and ODEs) ◮ Linear Algebra ◮ Abstract Algebra (up to the definition of a group) ◮ Sequences and Series ◮ Mechanics ◮ Statistics ◮ Discrete Maths ◮ Numerics ◮ MOMD

1st yr Calculus and Linear Algebra lectures ≈ 250 students Examples classes 15 to 30 students

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 7 / 25

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SLIDE 21

Programme Structure

120 credits in 10 credit blocks 100 credits passed at 40% to progress to Yr2 Content of year 1

◮ Calculus (up to integration and ODEs) ◮ Linear Algebra ◮ Abstract Algebra (up to the definition of a group) ◮ Sequences and Series ◮ Mechanics ◮ Statistics ◮ Discrete Maths ◮ Numerics ◮ MOMD

1st yr Calculus and Linear Algebra lectures ≈ 250 students Examples classes 15 to 30 students

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 7 / 25

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SLIDE 22

Issues particular to the U.K.

Students choose their major on application at age 17. They are “trapped". Lectures not section teaching: cost of teaching so intensively. Curriculum includes teaching and assessment style. Change needs approval. Emphasis on internal and external quality assurance. Greater emphasis on uniformity of assessment than in US.

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 8 / 25

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SLIDE 23

Issues particular to the U.K.

Students choose their major on application at age 17. They are “trapped". Lectures not section teaching: cost of teaching so intensively. Curriculum includes teaching and assessment style. Change needs approval. Emphasis on internal and external quality assurance. Greater emphasis on uniformity of assessment than in US.

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 8 / 25

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SLIDE 24

Issues particular to the U.K.

Students choose their major on application at age 17. They are “trapped". Lectures not section teaching: cost of teaching so intensively. Curriculum includes teaching and assessment style. Change needs approval. Emphasis on internal and external quality assurance. Greater emphasis on uniformity of assessment than in US.

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 8 / 25

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SLIDE 25

Issues particular to the U.K.

Students choose their major on application at age 17. They are “trapped". Lectures not section teaching: cost of teaching so intensively. Curriculum includes teaching and assessment style. Change needs approval. Emphasis on internal and external quality assurance. Greater emphasis on uniformity of assessment than in US.

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 8 / 25

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SLIDE 26

Issues particular to the U.K.

Students choose their major on application at age 17. They are “trapped". Lectures not section teaching: cost of teaching so intensively. Curriculum includes teaching and assessment style. Change needs approval. Emphasis on internal and external quality assurance. Greater emphasis on uniformity of assessment than in US.

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 8 / 25

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SLIDE 27

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 9 / 25

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SLIDE 28

Course setup

Quite close to Moore Method in structure. Aim is to develop problem solving and raise confidence, not to “cover stuff". Set up by Chris Good in 2004 Point set topology (3 years) Taken over by Chris Sangwin in 2007 Geometry (4 years) Taught by Chris Sangwin & Corneliau Hoffmann 2009 Optional first year module, mostly mathematics majors. A 10–30 students a year.

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 10 / 25

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SLIDE 29

Course setup

Quite close to Moore Method in structure. Aim is to develop problem solving and raise confidence, not to “cover stuff". Set up by Chris Good in 2004 Point set topology (3 years) Taken over by Chris Sangwin in 2007 Geometry (4 years) Taught by Chris Sangwin & Corneliau Hoffmann 2009 Optional first year module, mostly mathematics majors. A 10–30 students a year.

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 10 / 25

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SLIDE 30

Course setup

Quite close to Moore Method in structure. Aim is to develop problem solving and raise confidence, not to “cover stuff". Set up by Chris Good in 2004 Point set topology (3 years) Taken over by Chris Sangwin in 2007 Geometry (4 years) Taught by Chris Sangwin & Corneliau Hoffmann 2009 Optional first year module, mostly mathematics majors. A 10–30 students a year.

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 10 / 25

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SLIDE 31

Course setup

Quite close to Moore Method in structure. Aim is to develop problem solving and raise confidence, not to “cover stuff". Set up by Chris Good in 2004 Point set topology (3 years) Taken over by Chris Sangwin in 2007 Geometry (4 years) Taught by Chris Sangwin & Corneliau Hoffmann 2009 Optional first year module, mostly mathematics majors. A 10–30 students a year.

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 10 / 25

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SLIDE 32

Course setup

Quite close to Moore Method in structure. Aim is to develop problem solving and raise confidence, not to “cover stuff". Set up by Chris Good in 2004 Point set topology (3 years) Taken over by Chris Sangwin in 2007 Geometry (4 years) Taught by Chris Sangwin & Corneliau Hoffmann 2009 Optional first year module, mostly mathematics majors. A 10–30 students a year.

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 10 / 25

slide-33
SLIDE 33

Course setup

Quite close to Moore Method in structure. Aim is to develop problem solving and raise confidence, not to “cover stuff". Set up by Chris Good in 2004 Point set topology (3 years) Taken over by Chris Sangwin in 2007 Geometry (4 years) Taught by Chris Sangwin & Corneliau Hoffmann 2009 Optional first year module, mostly mathematics majors. A 10–30 students a year.

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 10 / 25

slide-34
SLIDE 34

Course setup

Quite close to Moore Method in structure. Aim is to develop problem solving and raise confidence, not to “cover stuff". Set up by Chris Good in 2004 Point set topology (3 years) Taken over by Chris Sangwin in 2007 Geometry (4 years) Taught by Chris Sangwin & Corneliau Hoffmann 2009 Optional first year module, mostly mathematics majors. A 10–30 students a year.

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 10 / 25

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SLIDE 35

Programme structure and assessment

Students take 120 credits per year. This course is 20 credits, split over two semesters. Semester 1 traditional geometry course. Semester 2 Moore method course. Quality of best 2 presentations 13% Individual written solutions to all problems 12% Examination 25% (Semester 1 “Formal Euclidean Geometry" 50%).

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 11 / 25

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SLIDE 36

Programme structure and assessment

Students take 120 credits per year. This course is 20 credits, split over two semesters. Semester 1 traditional geometry course. Semester 2 Moore method course. Quality of best 2 presentations 13% Individual written solutions to all problems 12% Examination 25% (Semester 1 “Formal Euclidean Geometry" 50%).

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 11 / 25

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SLIDE 37

Programme structure and assessment

Students take 120 credits per year. This course is 20 credits, split over two semesters. Semester 1 traditional geometry course. Semester 2 Moore method course. Quality of best 2 presentations 13% Individual written solutions to all problems 12% Examination 25% (Semester 1 “Formal Euclidean Geometry" 50%).

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 11 / 25

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SLIDE 38

Choice of problems

Taken from V. Gutenmacher and N.B. Vasilyev. Lines and curves: a practical geometry handbook. Birkhauser, 2004.

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 12 / 25

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SLIDE 39

Reasons

Geometry Locus problems, kinematics, (machine motion) Modelling aspects Little prior knowledge Often different solution approaches Example: the cat on the ladder 0.1 A ladder standing on a smooth floor against a wall slides down to the floor. Along what curve does a cat sitting in the middle of the ladder move?

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 13 / 25

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SLIDE 40

Reasons

Geometry Locus problems, kinematics, (machine motion) Modelling aspects Little prior knowledge Often different solution approaches Example: the cat on the ladder 0.1 A ladder standing on a smooth floor against a wall slides down to the floor. Along what curve does a cat sitting in the middle of the ladder move?

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 13 / 25

slide-41
SLIDE 41

Reasons

Geometry Locus problems, kinematics, (machine motion) Modelling aspects Little prior knowledge Often different solution approaches Example: the cat on the ladder 0.1 A ladder standing on a smooth floor against a wall slides down to the floor. Along what curve does a cat sitting in the middle of the ladder move?

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 13 / 25

slide-42
SLIDE 42

Reasons

Geometry Locus problems, kinematics, (machine motion) Modelling aspects Little prior knowledge Often different solution approaches Example: the cat on the ladder 0.1 A ladder standing on a smooth floor against a wall slides down to the floor. Along what curve does a cat sitting in the middle of the ladder move?

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 13 / 25

slide-43
SLIDE 43

Reasons

Geometry Locus problems, kinematics, (machine motion) Modelling aspects Little prior knowledge Often different solution approaches Example: the cat on the ladder 0.1 A ladder standing on a smooth floor against a wall slides down to the floor. Along what curve does a cat sitting in the middle of the ladder move?

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 13 / 25

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SLIDE 44

Reasons

Geometry Locus problems, kinematics, (machine motion) Modelling aspects Little prior knowledge Often different solution approaches Example: the cat on the ladder 0.1 A ladder standing on a smooth floor against a wall slides down to the floor. Along what curve does a cat sitting in the middle of the ladder move?

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 13 / 25

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SLIDE 45

CS’s reflections, 4 years

Surprising consistency and stability. Each year we have ended up 40 ± 2 problems from the same place. (35 pages out of 148) Week 1 Anticipation. Week 2 Excitement and enthusiasm. Week 3 Frustration. Week 4-5 Despondency, Doldrums and Despair. Week 6-7 Re-build confidence. Week 8-9 Adjust expectations. Week 10-11 Collegiate conviviality

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 14 / 25

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SLIDE 46

CS’s reflections, 4 years

Surprising consistency and stability. Each year we have ended up 40 ± 2 problems from the same place. (35 pages out of 148) Week 1 Anticipation. Week 2 Excitement and enthusiasm. Week 3 Frustration. Week 4-5 Despondency, Doldrums and Despair. Week 6-7 Re-build confidence. Week 8-9 Adjust expectations. Week 10-11 Collegiate conviviality

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 14 / 25

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SLIDE 47

CS’s reflections, 4 years

Surprising consistency and stability. Each year we have ended up 40 ± 2 problems from the same place. (35 pages out of 148) Week 1 Anticipation. Week 2 Excitement and enthusiasm. Week 3 Frustration. Week 4-5 Despondency, Doldrums and Despair. Week 6-7 Re-build confidence. Week 8-9 Adjust expectations. Week 10-11 Collegiate conviviality

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 14 / 25

slide-48
SLIDE 48

CS’s reflections, 4 years

Surprising consistency and stability. Each year we have ended up 40 ± 2 problems from the same place. (35 pages out of 148) Week 1 Anticipation. Week 2 Excitement and enthusiasm. Week 3 Frustration. Week 4-5 Despondency, Doldrums and Despair. Week 6-7 Re-build confidence. Week 8-9 Adjust expectations. Week 10-11 Collegiate conviviality

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 14 / 25

slide-49
SLIDE 49

CS’s reflections, 4 years

Surprising consistency and stability. Each year we have ended up 40 ± 2 problems from the same place. (35 pages out of 148) Week 1 Anticipation. Week 2 Excitement and enthusiasm. Week 3 Frustration. Week 4-5 Despondency, Doldrums and Despair. Week 6-7 Re-build confidence. Week 8-9 Adjust expectations. Week 10-11 Collegiate conviviality

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 14 / 25

slide-50
SLIDE 50

CS’s reflections, 4 years

Surprising consistency and stability. Each year we have ended up 40 ± 2 problems from the same place. (35 pages out of 148) Week 1 Anticipation. Week 2 Excitement and enthusiasm. Week 3 Frustration. Week 4-5 Despondency, Doldrums and Despair. Week 6-7 Re-build confidence. Week 8-9 Adjust expectations. Week 10-11 Collegiate conviviality

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 14 / 25

slide-51
SLIDE 51

CS’s reflections, 4 years

Surprising consistency and stability. Each year we have ended up 40 ± 2 problems from the same place. (35 pages out of 148) Week 1 Anticipation. Week 2 Excitement and enthusiasm. Week 3 Frustration. Week 4-5 Despondency, Doldrums and Despair. Week 6-7 Re-build confidence. Week 8-9 Adjust expectations. Week 10-11 Collegiate conviviality

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 14 / 25

slide-52
SLIDE 52

CS’s reflections, 4 years

Surprising consistency and stability. Each year we have ended up 40 ± 2 problems from the same place. (35 pages out of 148) Week 1 Anticipation. Week 2 Excitement and enthusiasm. Week 3 Frustration. Week 4-5 Despondency, Doldrums and Despair. Week 6-7 Re-build confidence. Week 8-9 Adjust expectations. Week 10-11 Collegiate conviviality

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 14 / 25

slide-53
SLIDE 53

CS’s reflections, 4 years

Surprising consistency and stability. Each year we have ended up 40 ± 2 problems from the same place. (35 pages out of 148) Week 1 Anticipation. Week 2 Excitement and enthusiasm. Week 3 Frustration. Week 4-5 Despondency, Doldrums and Despair. Week 6-7 Re-build confidence. Week 8-9 Adjust expectations. Week 10-11 Collegiate conviviality

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 14 / 25

slide-54
SLIDE 54

Quantitative Study

We want to determine whether 1Y has any effect on students’ performances in other modules in the School of Mathematics. 6494 module results from 947 students over nine academic years were used for quantitative analysis. We could use independent t-tests to compare the mean scores of 1Y and non-1Y students. 1Y students are a self-selecting group

t-test for Equality of Means 95% Confidence Equal Sig. Mean

  • Std. Error

Interval Variances t df (2-tailed) Difference Difference Lower Upper 1Aa Mark Assumed

  • 4.59

826 0.0000

  • 11.96

2.60

  • 17.08
  • 6.85

Not assumed

  • 5.31

49 0.0000

  • 11.96

2.25

  • 16.49
  • 7.44

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 16 / 25

slide-55
SLIDE 55

Quantitative Study

We want to determine whether 1Y has any effect on students’ performances in other modules in the School of Mathematics. 6494 module results from 947 students over nine academic years were used for quantitative analysis. We could use independent t-tests to compare the mean scores of 1Y and non-1Y students. 1Y students are a self-selecting group

t-test for Equality of Means 95% Confidence Equal Sig. Mean

  • Std. Error

Interval Variances t df (2-tailed) Difference Difference Lower Upper 1Aa Mark Assumed

  • 4.59

826 0.0000

  • 11.96

2.60

  • 17.08
  • 6.85

Not assumed

  • 5.31

49 0.0000

  • 11.96

2.25

  • 16.49
  • 7.44

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 16 / 25

slide-56
SLIDE 56

Quantitative Study

We want to determine whether 1Y has any effect on students’ performances in other modules in the School of Mathematics. 6494 module results from 947 students over nine academic years were used for quantitative analysis. We could use independent t-tests to compare the mean scores of 1Y and non-1Y students. 1Y students are a self-selecting group

t-test for Equality of Means 95% Confidence Equal Sig. Mean

  • Std. Error

Interval Variances t df (2-tailed) Difference Difference Lower Upper 1Aa Mark Assumed

  • 4.59

826 0.0000

  • 11.96

2.60

  • 17.08
  • 6.85

Not assumed

  • 5.31

49 0.0000

  • 11.96

2.25

  • 16.49
  • 7.44

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 16 / 25

slide-57
SLIDE 57

Quantitative Study

Linear regression allows us to remove the effect of 1Y students being better to begin with. We predict first year results using 1Aa class test mark and 1Y participation We predict second year results using first year mean and 1Y participation The models have the equation Module mark = β0 + β1CT + β2Y. Third year results were inconclusive - too little data to for significant results

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 17 / 25

slide-58
SLIDE 58

Quantitative Study

Linear regression allows us to remove the effect of 1Y students being better to begin with. We predict first year results using 1Aa class test mark and 1Y participation We predict second year results using first year mean and 1Y participation The models have the equation Module mark = β0 + β1CT + β2Y. Third year results were inconclusive - too little data to for significant results

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 17 / 25

slide-59
SLIDE 59

Quantitative Study

Linear regression allows us to remove the effect of 1Y students being better to begin with. We predict first year results using 1Aa class test mark and 1Y participation We predict second year results using first year mean and 1Y participation The models have the equation Module mark = β0 + β1CT + β2Y. Third year results were inconclusive - too little data to for significant results

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 17 / 25

slide-60
SLIDE 60

Quantitative Study

Linear regression allows us to remove the effect of 1Y students being better to begin with. We predict first year results using 1Aa class test mark and 1Y participation We predict second year results using first year mean and 1Y participation The models have the equation Module mark = β0 + β1CT + β2Y. Third year results were inconclusive - too little data to for significant results

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 17 / 25

slide-61
SLIDE 61

Quantitative Study

Linear regression allows us to remove the effect of 1Y students being better to begin with. We predict first year results using 1Aa class test mark and 1Y participation We predict second year results using first year mean and 1Y participation The models have the equation Module mark = β0 + β1CT + β2Y. Third year results were inconclusive - too little data to for significant results

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 17 / 25

slide-62
SLIDE 62

Quantitative Results

First year regressions

Module Subject Areas 1Y Coeff. F-Test Sig. 1Aa Calculus, Geometry, Matrices 4.47 (1.81) 0.014 1Ab Calculus and Algebra 7.00 (2.70) 0.010 1B Number Theory, Sequences & Series 7.37 (2.26) 0.001 1C Mechanics & Computational Math(s)

  • 0.04 (2.40)

0.987 1D Discrete Math(s) and Statistics 3.60 (2.36) 0.127

Second year regressions

Module Subject Areas 1Y Coeff. F-Test Sig. 203 Polynomials, Rings & Metric Spaces 7.62 (3.64) 0.038 2B Real and Complex Variable Theory 4.50 (2.48) 0.071 2C Linear Algebra & Programming 4.04 (2.53) 0.110

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 18 / 25

slide-63
SLIDE 63

Quantitative Results

First year regressions

Module Subject Areas 1Y Coeff. F-Test Sig. 1Aa Calculus, Geometry, Matrices 4.47 (1.81) 0.014 1Ab Calculus and Algebra 7.00 (2.70) 0.010 1B Number Theory, Sequences & Series 7.37 (2.26) 0.001 1C Mechanics & Computational Math(s)

  • 0.04 (2.40)

0.987 1D Discrete Math(s) and Statistics 3.60 (2.36) 0.127

Second year regressions

Module Subject Areas 1Y Coeff. F-Test Sig. 203 Polynomials, Rings & Metric Spaces 7.62 (3.64) 0.038 2B Real and Complex Variable Theory 4.50 (2.48) 0.071 2C Linear Algebra & Programming 4.04 (2.53) 0.110

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 18 / 25

slide-64
SLIDE 64

Qualitative Work

Quantitative results are interesting . . . . . . but improving marks in other modules was not the main motivation for introducing the course So what do students tell us1?

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 19 / 25

slide-65
SLIDE 65

Qualitative Work

Quantitative results are interesting . . . . . . but improving marks in other modules was not the main motivation for introducing the course So what do students tell us1?

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 19 / 25

slide-66
SLIDE 66

Qualitative Work

Quantitative results are interesting . . . . . . but improving marks in other modules was not the main motivation for introducing the course So what do students tell us1?

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 19 / 25

slide-67
SLIDE 67

Qualitative Work

Quantitative results are interesting . . . . . . but improving marks in other modules was not the main motivation for introducing the course So what do students tell us1

1A (hopefully) representative sample bound by the strictures of biased

  • bservers

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 20 / 25

slide-68
SLIDE 68

What is proof?

Results: end of course questionnaires in 2008 and 2011 Typical answers: a logical step by step argument that, with no unnecessary steps, that shows without a doubt that the statement is true. A mathematical proof is a deductive process where, starting from already proven theorems and other facts, we can deduce through a series of undisputable steps a required result.

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 21 / 25

slide-69
SLIDE 69

What is proof?

Results: end of course questionnaires in 2008 and 2011 Typical answers: a logical step by step argument that, with no unnecessary steps, that shows without a doubt that the statement is true. A mathematical proof is a deductive process where, starting from already proven theorems and other facts, we can deduce through a series of undisputable steps a required result.

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 21 / 25

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SLIDE 70

Has your concepts of proof changed?

Yep! At first my idea was of a proof was writing long chunks of work and simplity hoping the correct proof was in there. As I gained more experience I found a good proof is consise and to the point. Rather then writing pages and pages for a proof with unnessary info I learnt to shorten my work down to say a page with just the nessary info. that it is not necessarily a long winded argument and the most satisfying proof is a short one. Yes, I use to feel that the complicated long proofs always were the ‘best’ i can now appreciate that this is far from true.

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 22 / 25

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SLIDE 71

Did anything in the course surprise you?

The amount of work and how hard it was. It surprised me how much I learnt without really any direct

  • teaching. I was expecting to be taught topics and then be set

problems based on those topics but the self-taught approach was much more effective that I would have anticipated. Not sure if it counts as an event, but just the fact that i actually really enjoyed geometry. Before the course i would have said I didn’t like it at all, but now i realise this is not ture, and really wish I could do geometry next year. Thales theorem may as well be the meaning of life at this rate.

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 23 / 25

slide-72
SLIDE 72

Not all students engaged...

Overall i think that it is an extremly interesting course and in a way wish i had turned up to more lectures and given it alot more time. When signing up i had no idea how much hardwork it would be and deffinitly sturggled to keep up with the pace of the course. It is obviopusly my fault that i failed and will have to retake it as i failed to turn up to most of the lectures but think that its a tiny bit unfair that people gained 20 credits doing the other maths course which could have easily passed with out paying much attention [. . . ] I think the main probelm is that a momd at birmingham is sort

  • f seen as abit of a joke and easy credits but y is deffinitly not

that. [. . . ] Anyway sorry if that seems a tiny bit direct and rude as i dont want to come arcross that way as i do think it was a very well run course, just probably one i shouldn’t have done. Thank you anyway.

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 24 / 25

slide-73
SLIDE 73

Not all students engaged...

Overall i think that it is an extremly interesting course and in a way wish i had turned up to more lectures and given it alot more time. When signing up i had no idea how much hardwork it would be and deffinitly sturggled to keep up with the pace of the course. It is obviopusly my fault that i failed and will have to retake it as i failed to turn up to most of the lectures but think that its a tiny bit unfair that people gained 20 credits doing the other maths course which could have easily passed with out paying much attention [. . . ] I think the main probelm is that a momd at birmingham is sort

  • f seen as abit of a joke and easy credits but y is deffinitly not

that. [. . . ] Anyway sorry if that seems a tiny bit direct and rude as i dont want to come arcross that way as i do think it was a very well run course, just probably one i shouldn’t have done. Thank you anyway.

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 24 / 25

slide-74
SLIDE 74

Not all students engaged...

Overall i think that it is an extremly interesting course and in a way wish i had turned up to more lectures and given it alot more time. When signing up i had no idea how much hardwork it would be and deffinitly sturggled to keep up with the pace of the course. It is obviopusly my fault that i failed and will have to retake it as i failed to turn up to most of the lectures but think that its a tiny bit unfair that people gained 20 credits doing the other maths course which could have easily passed with out paying much attention [. . . ] I think the main probelm is that a momd at birmingham is sort

  • f seen as abit of a joke and easy credits but y is deffinitly not

that. [. . . ] Anyway sorry if that seems a tiny bit direct and rude as i dont want to come arcross that way as i do think it was a very well run course, just probably one i shouldn’t have done. Thank you anyway.

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 24 / 25

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SLIDE 75

Conclusion

Importance of staff ownership. Large lectures in years 1 & 2 mean structural support required. Evidence of efficacy

◮ quantitative & ◮ qualitative, (delayed post-testing, social, affective, etc.)

It can be difficult to convince colleagues. “It is a luxury we can’t afford" We can’t afford to omit it! Some students fail to engage. They are trapped .... stakes are very high. The future. . .

◮ All MSci (four year masters) students will be required to take 1Y

starting this autumn

◮ University of Leicester has introduced a “Moore Method” course in

its first year, but individual staff have a lot of say in its organisation and it does not follow a single strict pedagogy.

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 25 / 25

slide-76
SLIDE 76

Conclusion

Importance of staff ownership. Large lectures in years 1 & 2 mean structural support required. Evidence of efficacy

◮ quantitative & ◮ qualitative, (delayed post-testing, social, affective, etc.)

It can be difficult to convince colleagues. “It is a luxury we can’t afford" We can’t afford to omit it! Some students fail to engage. They are trapped .... stakes are very high. The future. . .

◮ All MSci (four year masters) students will be required to take 1Y

starting this autumn

◮ University of Leicester has introduced a “Moore Method” course in

its first year, but individual staff have a lot of say in its organisation and it does not follow a single strict pedagogy.

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 25 / 25

slide-77
SLIDE 77

Conclusion

Importance of staff ownership. Large lectures in years 1 & 2 mean structural support required. Evidence of efficacy

◮ quantitative & ◮ qualitative, (delayed post-testing, social, affective, etc.)

It can be difficult to convince colleagues. “It is a luxury we can’t afford" We can’t afford to omit it! Some students fail to engage. They are trapped .... stakes are very high. The future. . .

◮ All MSci (four year masters) students will be required to take 1Y

starting this autumn

◮ University of Leicester has introduced a “Moore Method” course in

its first year, but individual staff have a lot of say in its organisation and it does not follow a single strict pedagogy.

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 25 / 25

slide-78
SLIDE 78

Conclusion

Importance of staff ownership. Large lectures in years 1 & 2 mean structural support required. Evidence of efficacy

◮ quantitative & ◮ qualitative, (delayed post-testing, social, affective, etc.)

It can be difficult to convince colleagues. “It is a luxury we can’t afford" We can’t afford to omit it! Some students fail to engage. They are trapped .... stakes are very high. The future. . .

◮ All MSci (four year masters) students will be required to take 1Y

starting this autumn

◮ University of Leicester has introduced a “Moore Method” course in

its first year, but individual staff have a lot of say in its organisation and it does not follow a single strict pedagogy.

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 25 / 25

slide-79
SLIDE 79

Conclusion

Importance of staff ownership. Large lectures in years 1 & 2 mean structural support required. Evidence of efficacy

◮ quantitative & ◮ qualitative, (delayed post-testing, social, affective, etc.)

It can be difficult to convince colleagues. “It is a luxury we can’t afford" We can’t afford to omit it! Some students fail to engage. They are trapped .... stakes are very high. The future. . .

◮ All MSci (four year masters) students will be required to take 1Y

starting this autumn

◮ University of Leicester has introduced a “Moore Method” course in

its first year, but individual staff have a lot of say in its organisation and it does not follow a single strict pedagogy.

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 25 / 25

slide-80
SLIDE 80

Conclusion

Importance of staff ownership. Large lectures in years 1 & 2 mean structural support required. Evidence of efficacy

◮ quantitative & ◮ qualitative, (delayed post-testing, social, affective, etc.)

It can be difficult to convince colleagues. “It is a luxury we can’t afford" We can’t afford to omit it! Some students fail to engage. They are trapped .... stakes are very high. The future. . .

◮ All MSci (four year masters) students will be required to take 1Y

starting this autumn

◮ University of Leicester has introduced a “Moore Method” course in

its first year, but individual staff have a lot of say in its organisation and it does not follow a single strict pedagogy.

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 25 / 25

slide-81
SLIDE 81

Conclusion

Importance of staff ownership. Large lectures in years 1 & 2 mean structural support required. Evidence of efficacy

◮ quantitative & ◮ qualitative, (delayed post-testing, social, affective, etc.)

It can be difficult to convince colleagues. “It is a luxury we can’t afford" We can’t afford to omit it! Some students fail to engage. They are trapped .... stakes are very high. The future. . .

◮ All MSci (four year masters) students will be required to take 1Y

starting this autumn

◮ University of Leicester has introduced a “Moore Method” course in

its first year, but individual staff have a lot of say in its organisation and it does not follow a single strict pedagogy.

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 25 / 25

slide-82
SLIDE 82

Conclusion

Importance of staff ownership. Large lectures in years 1 & 2 mean structural support required. Evidence of efficacy

◮ quantitative & ◮ qualitative, (delayed post-testing, social, affective, etc.)

It can be difficult to convince colleagues. “It is a luxury we can’t afford" We can’t afford to omit it! Some students fail to engage. They are trapped .... stakes are very high. The future. . .

◮ All MSci (four year masters) students will be required to take 1Y

starting this autumn

◮ University of Leicester has introduced a “Moore Method” course in

its first year, but individual staff have a lot of say in its organisation and it does not follow a single strict pedagogy.

Chris Good, Chris Sangwin, Matthew Badger (University of Birmingham) The Moore Method in the U.K.: IBL at Birmingham June 2011 25 / 25